2017/10/03 by Shiquan Ruan, Ruan, Shiquan, Xintian Wang +1 · 1 citation
Physics and Astronomy · Mathematics · #Advanced Differential Geometry Research #Advanced Differential Equations and Dynamical Systems #Geometric Analysis and Curvature Flows
paper · pdf · doi:10.48550/arxiv.1710.00986
The present paper focuses on the study of t-stabilities on a triangulated category in the sense of Gorodentsev, Kuleshov and Rudakov. We give an equivalent description for the finest t-stability on a piecewise hereditary triangulated category and, describe the semistable subcategories and final HN triangles for (exceptional) coherent sheaves in Db(\rmcoh\mathbbX), which is the bounded derived category of coherent sheaves on the weighted projective line \mathbbX of weight type (2). Furthermore, we show the existence of a t-exceptional triple for Db(\rmcoh\mathbbX). As an application, we obtain a result of Dimitrov--Katzarkov which states that each stability condition σ in the sense of Bridgeland admits a σ-exceptional triple for the acyclic triangular quiver Q. Note that this implies the connectedness of the space of stability conditions associated to Q.